Projectile Motion - Real-life applications

Photo by: Kletr

Bullets on a Straight Spinning Flight

One of the first things people think of when they hear the word
"ballistics" is the study of gunfire patterns for the
purposes of crime-solving. Indeed, this application of ballistics is a
significant part of police science, because it allows law-enforcement
investigators to determine when, where, and how a firearm was used. In
a larger sense, however, the term as applied to firearms refers to
efforts toward creating a more effective, predictable, and longer
bullet trajectory.

From the advent of firearms in the West during the fourteenth century
until about 1500, muskets were hopelessly unreliable. This was because
the lead balls they fired had not been fitted to the barrel of the
musket. When fired, they bounced erratically off the sides of the
barrel, and this made their trajectories unpredictable. Compounding
this was the unevenness of the lead balls themselves, and this
irregularity of shape could lead to even greater irregularities in
trajectory.

Around 1500, however, the first true rifles appeared, and these
greatly enhanced the accuracy of firearms. The term rifle comes from
the "rifling" of the musket barrels: that is, the
barrels themselves were engraved with grooves, a process known as
rifling. Furthermore, ammunition-makers worked to improve the
production process where the musket balls were concerned, producing
lead rounds that were more uniform in shape and size.

Despite these improvements, soldiers over the next three centuries
still faced many challenges when firing lead balls from rifled
barrels. The lead balls themselves, because they were made of a soft
material, tended to become misshapen during the loading process.
Furthermore, the gunpowder that propelled the lead balls had a
tendency to clog the rifle barrel. Most important of all was the fact
that these rifles took time to load—and in a situation of
battle, this could cost a man his life.

The first significant change came in the 1840s, when in place of lead
balls, armies began using bullets. The difference in shape greatly
improved the response of rounds to aerodynamic factors. In 1847,
Claude-Etienne Minié, a captain in the French army, developed a
bullet made of lead, but with a base that was slightly hollow. Thus
when fired, the lead in the round tended to expand, filling the
barrel's diameter and gripping the rifling.

As a result, the round came out of the barrel end spinning, and
continued to spin throughout its flight. Not only were soldiers able
to fire their rifles with much greater accuracy, but thanks to the
development of chambers and magazines, they could reload more quickly.

Curve Balls, Dimpled Golf Balls, and Other Tricks with Spin

In the case of a bullet, spin increases accuracy, ensuring that the
trajectory will follow an expected path. But sometimes spin can be
used in more complex ways, as with a curveball thrown by a baseball
pitcher.

The invention of the curveball is credited to Arthur
"Candy" Cummings, who as a pitcher for the Brooklyn
Excelsiors at the age of 18 in 1867—an era when baseball was
still very young—introduced a new throw he had spent several
years perfecting. Snapping as he released the ball, he and the
spectators (not to mention the startled batter for the opposing team)
watched as the pitch arced, then sailed right past the batter for a
strike.

The curveball bedeviled baseball players and fans alike for many years
thereafter, and many dismissed it as a type of optical illusion. The
debate became so heated that in 1941, both
Life
and
Look
magazines ran features using stop-action photography to show that a
curveball truly did curve. Even in 1982, a team of researchers from
General Motors (GM) and the Massachusetts Institute of Technology
(MIT), working at the behest of
Science
magazine, investigated the curveball to determine if it was more than
a mere trick.

In fact, the curveball is a trick, but there is nothing fake about it.
As the pitcher releases the ball, he snaps his wrist. This puts a spin
on the projectile, and air resistance does the rest. As the ball moves
toward the plate, its spin moves against the air, which creates an
airstream moving against the trajectory of the ball itself. The
airstream splits into two lines, one curving over the ball and one
curving under, as the ball sails toward home plate.

For the purposes of clarity, assume that you are viewing the throw
from a position between third base and home. Thus, the ball is moving
from left to right, and therefore the direction of airflow is from
right to left. Meanwhile the ball, as it moves into the airflow, is
spinning clockwise. This means that the air flowing over the top of
the ball is moving in a direction opposite to the spin, whereas that
flowing under it is moving in the same direction as the spin.

This creates an interesting situation, thanks to Bernoulli's
principle. The latter, formulated by Swiss mathematician and physicist
Daniel Bernoulli (1700-1782), holds that where velocity is high,
pressure is low—and vice versa. Bernoulli's principle is
of the utmost importance to aerodynamics, and likewise plays a
significant role in the operation of a curveball. At the top of the

G
OLF BALLS ARE DIMPLED BECAUSE THEY TRAVEL MUCH FARTHER THAN
NONDIMPLED ONES
.
(Photograph by

D. Boone/Corbis

.
Reproduced by permission.)

ball, its clockwise spin is moving in a direction opposite to the
airflow. This produces drag, slowing the ball, increasing pressure,
and thus forcing it downward. At the bottom end of the ball, however,
the clockwise motion is flowing with the air, thus resulting in higher
velocity and lower pressure. As per Bernoulli's principle, this
tends to pull the ball downward.

In the 60-ft, 6-in (18.4-m) distance that separates the
pitcher's mound from home plate on a regulation major-league
baseball field, a curve-ball can move downward by a foot (0.3048 m) or
more. The interesting thing here is that this downward force is almost
entirely due to air resistance rather than gravity, though of course
gravity eventually brings any pitch to the ground, assuming it has not
already been hit, caught, or bounced off a fence.

A curveball represents a case in which spin is used to deceive the
batter, but it is just as possible that a pitcher may create havoc at
home plate by throwing a ball with little or no spin. This is called a
knuckleball, and it is based on the fact that spin in
general—though certainly not the deliberate spin of a
curveball—tends to ensure a more regular trajectory. Because a
knuckleball has no spin, it follows an apparently random path, and
thus it can be every bit as tricky for the pitcher as for the batter.

Golf, by contrast, is a sport in which spin is expected: from the
moment a golfer hits the ball, it spins backward—and this in
turn helps to explain why golf balls are dimpled. Early golf balls,
known as featheries, were merely smooth leather pouches containing
goose feathers. The smooth surface seemed to produce relatively low
drag, and golfers were impressed that a well-hit feathery could travel
150-175 yd (137-160 m).

Then in the late nineteenth century, a professor at St. Andrews
University in Scotland realized that a scored or marked ball would
travel farther than a smooth one. (The part about St. Andrews may
simply be golfing legend, since the course there is regarded as the
birthplace of golf in the fifteenth century.) Whatever the case, it is
true that a scored ball has a longer trajectory, again as a result of
the effect of air resistance on projectile motion.

Airflow produces two varieties of drag on a sphere such as a golf
ball: drag due to friction, which is only a small aspect of the total
drag, and the much more significant drag that results from the
separation of airflow around the ball. As with the curveball discussed
earlier, air flows above and below the ball, but the issue here is
more complicated than for the curved pitch.

Airflow comes in two basic varieties: laminar, meaning streamlined; or
turbulent, indicating an erratic, unpredictable flow. For a jet flying
through the air, it is most desirable to create a laminar flow passing
over its airfoil, or the curved front surface of the wing. In the case
of the golf ball, however, turbulent flow is more desirable.

In laminar flow, the airflow separates quickly, part of it passing
over the ball and part passing under. In turbulent flow, however,
separation comes later, further back on the ball. Each form of air
separation produces a separation region, an area of drag that the ball
pulls behind it (so to speak) as it flies through space. But because
the separation comes further back on the ball in turbulent flow, the
separation region itself is narrower, thus producing less drag.

Clearly, scoring the ball produced turbulent flow, and for a few years
in the early twentieth century, manufacturers experimented with
designs that included squares, rectangles, and hexagons. In time, they
settled on the dimpled design known today. Golf balls made in Britain
have 330 dimples, and those in America 336; in either case, the
typical drive distance is much, much further than for an unscored
ball—180-250 yd (165-229 m).

Powered Projectiles: Rockets and Missiles

The most complex form of projectile widely known in modern life is the
rocket or missile. Missiles are unmanned vehicles, most often used in
warfare to direct some form of explosive toward an enemy. Rockets, on
the other hand, can be manned or unmanned, and may be propulsion
vehicles for missiles or for spacecraft. The term rocket can refer
either to the engine or to the vehicle it propels.

The first rockets appeared in China during the late medieval period,
and were used unsuccessfully by the Chinese against Mongol invaders in
the early part of the thirteenth century. Europeans later adopted
rocketry for battle, as for instance when French forces under Joan of
Arc used crude rockets in an effort to break the siege on Orleans in
1429.

Within a century or so, however, rocketry as a form of military
technology became obsolete, though projectile warfare itself remained
as effective a method as ever. From the catapults of Roman times to
the cannons that appeared in the early Renaissance to the heavy
artillery of today, armies have been shooting projectiles against
their enemies. The crucial difference between these projectiles and
rockets or missiles is that the latter varieties are self-propelled.

Only around the end of World War II did rocketry and missile warfare
begin to reappear in new, terrifying forms. Most notable among these
was Hitler's V-2 "rocket" (actually a missile),
deployed against Great Britain in 1944, but fortunately developed too
late to make an impact. The 1950s saw the appearance of nuclear
war-heads such as the ICBM (intercontinental ballistic missile). These
were guided missiles, as opposed to the V-2, which was essentially a
huge self-propelled bullet fired toward London.

More effective than the ballistic missile, however, was the cruise
missile, which appeared in later decades and which included
aerodynamic structures that assisted in guidance and

I
N THE CASE OF A ROCKET
,
LIKE THIS
P
ATRIOT MISSILE BEING LAUNCHED DURING A TEST
,
PROPULSION COMES BY EXPELLING FLUID
—
WHICH IN SCIENTIFIC TERMS CAN MEAN A GAS AS WELL AS A LIQUID
—
FROM ITS REAR END
. M
OST OFTEN THIS FLUID IS A MASS OF HOT GASES PRODUCED BY A
CHEMICAL REACTION INSIDE THE ROCKET
'
S BODY
,
AND THIS BACKWARD MOTION CREATES AN EQUAL AND OPPOSITE REACTION
FROM THE ATMOSPHERE
,
PROPELLING THE ROCKET FORWARD
.

(Corbis

.
Reproduced by permission.)

maneuvering. In addition to guided or unguided, ballistic or
aerodynamic, missiles can be classified in terms of source and target:
surface-to-surface, air-to-air, and so on. By the 1970s, the United
States had developed an extraordinarily sophisticated surface-to-air
missile, the Stinger. Stingers proved a decisive factor in the
Afghan-Soviet War (1979-89), when U.S.-supplied Afghan guerrillas used
them against Soviet aircraft.

In the period from the late 1940s to the late 1980s, the United
States, the Soviet Union, and other smaller nuclear powers stockpiled
these warheads, which were most effective precisely because they were
never used. Thus, U.S. President Ronald Reagan played an important
role in ending the Cold War, because his weapons buildup forced the
Soviets to spend money they did not have on building their own
arsenal. During the aftermath of the Cold War, America and the newly
democratized Russian Federation worked to reduce their nuclear
stockpiles. Ironically, this was also the period when sophisticated
missiles such as the
Patriot
began gaining widespread use in the Persian Gulf War and later
conflicts.

Certain properties unite the many varieties of rocket that have
existed across time and space—including the relatively harmless
fireworks used in Fourth of July and New Year's Eve
celebrations around the country. One of the key principles that makes
rocket propulsion possible is the third law of motion. Sometimes
colloquially put as "For every action, there is an equal and
opposite reaction," a more scientifically accurate version of
this law would be: "When one object exerts a force on another,
the second object exerts on the first a force equal in magnitude but
opposite in direction."

In the case of a rocket, propulsion comes by expelling
fluid—which in scientific terms can mean a gas as well as a
liquid—from its rear. Most often this fluid is a mass of hot
gases produced by a chemical reaction inside the rocket's body,
and this backward motion creates an equal and opposite reaction from
the rocket, propelling it forward.

Before it undergoes a chemical reaction, rocket fuel may be either in
solid or liquid form inside the rocket's fuel chamber, though
it ends up as a gas when expelled. Both solid and liquid varieties
have their advantages and disadvantages in terms of safety,
convenience, and efficiency in lifting the craft. Scientists calculate
efficiency by a number of standards, among them specific impulse, a
measure of the mass that can be lifted by a particular type of fuel
for each pound of fuel consumed (that is, the rocket and its contents)
per second of operation time. Figures for specific impulse are
rendered in seconds.

A spacecraft may be divided into segments or stages, which can be
released as specific points along the flight in part to increase
specific impulse. This was the case with the
Saturn 5
rockets that carried astronauts to the Moon in the period 1969-72,
but not with the varieties of space shuttle that have flown regular
missions since 1981.

The space shuttle is essentially a hybrid of an airplane and rocket,
with a physical structure more like that of an aircraft but with
rocket power. In fact, the shuttle uses many rockets to maximize
efficiency, utilizing no less than 67 rockets—49 of which run
on liquid fuel and the rest on solid fuel—at different stages
of its flight.